Math 440, Fall 2014, Assignment 12

"Reeling and Writhing, of course, to begin with," the Mock Turtle replied; "And then the different branches of Arithmetic - Ambition, Distraction, Uglification, and Derision."

- Lewis Carroll, Alice's Adventures in Wonderland

Carefully define the following terms, then give one example and one non-example of each:

1. Totally disconnected (space).
2. Path component.
3. Locally pathwise connected (space).

Carefully state the following theorems (you need not prove them):

1. Theorem relating path-connectedness to connectedness in general.
2. Theorem relating path-connectedness to connectedness for locally pathwise connected spaces.

Solve the following problems:

1. Problem 27D(1-3).

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